Many everyday rhythmic activities, essential for life, such as breathing, chewing, and locomoting, are programed in part by central neuronal networks called central pattern generators (CPGs). Mechanistic analysis of CPGs has been especially fruitful in the numerically restricted CPGs of invertebrates, where networks can be precisely defined in terms of identified neurons and specific synaptic connections. Moreover, CPG networks of invertebrates have becomes proxies for experimental and theoretical analyses of how brain networks reliably, albeit plastically, process sensory information or program motor output. Our detailed analyses of the leech heartbeat CPG over the past 30 years have contributed to many of the organizing principles by which we now understand networks and their modulation. Starting with theoretical studies but now supported by experimental analysis in several different networks and species, we have come to realize that reliable network output can result from networks in which the intrinsic membrane properties (maximal conductances) of the neurons and the strengths of the synaptic connections can show 2-5 fold animal-to-animal variability. These studies imply that to understand fundamentally a neuronal network, we must gather as much as possible complete data from individuals, because networks from different individuals, while functionally indistinguishable, may have different mechanistic underpinnings at the level of membrane currents and synaptic connections. The reaction in the modeling community has ranged from a continued pursuance of 'ideal parameter sets' or sticking to averaged data for parameters to evolutionary algorithms for generating multiple functional models for testing or brute force parameter variation generating in some cases millions of functional models. The situation is still fluid, but experimental studies that document the extent of parameter variation in the living system and potential correlations among these parameters followed by computational analyses are clearly needed across a variety of networks. The proposed experiments will integrate computational and neurophysiological approaches to elucidate basic mechanisms of motor performance, motor control, and network function and the impact of individual variation in network parameters on these outcomes. Moreover, we will use individual variation as an innovative tool to probe network function. The leech heartbeat CPG is analogous to spinal CPGs that produce coordinated locomotor activity in motor neurons, and its relative simplicity and superb accessibility allow for detailed cellular analysis at the level of identified neurons and across a sample population of individuals. Understanding the organizing principles and the impact of individual variation in a well-characterized CPG network can provide basic mechanistic insights. Such insights derived from the study of invertebrate animals over the past 60 years have proven applicable to brain and spinal networks. In future they may be exploited to address clinical disorders such as those caused by injury or disease.